Nuprl Lemma : board-cell_wf
∀[T:Type]. ∀[n:ℕ]. ∀[b:square-board(n;T)]. ∀[i,j:ℕn]. (board-cell(b;i;j) ∈ T)
Proof
Definitions occuring in Statement :
board-cell: board-cell(b;i;j),
square-board: square-board(n;T),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
square-board: square-board(n;T),
board-cell: board-cell(b;i;j),
and: P ∧ Q,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
nat: ℕ,
ge: i ≥ j ,
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_weakening_equal,
true_wf,
squash_wf,
less_than_wf,
nat_wf,
square-board_wf,
int_seg_wf,
int_formula_prop_eq_lemma,
int_formula_prop_less_lemma,
intformeq_wf,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
int_seg_properties,
list_wf,
select_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
sqequalRule,
productElimination,
lemma_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
independent_isectElimination,
natural_numberEquality,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality,
universeEquality,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[b:square-board(n;T)]. \mforall{}[i,j:\mBbbN{}n]. (board-cell(b;i;j) \mmember{} T)
Date html generated:
2016_05_15-PM-03_13_58
Last ObjectModification:
2016_01_16-AM-10_47_52
Theory : general
Home
Index