Nuprl Lemma : fun-connected_weakening_eq
∀[T:Type]. ∀f:T ⟶ T. ∀x,y:T. y is f*(x) supposing x = y ∈ T
Proof
Definitions occuring in Statement :
fun-connected: y is f*(x),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
fun-connected: y is f*(x),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
exists: ∃x:A. B[x],
fun-path: y=f*(x) via L,
and: P ∧ Q,
top: Top,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
last: last(L),
subtract: n - m,
select: L[n],
cons: [a / b],
cand: A c∧ B,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A
Lemmas referenced :
equal_wf,
cons_wf,
nil_wf,
fun-path_wf,
length-singleton,
reduce_hd_cons_lemma,
length_of_cons_lemma,
length_of_nil_lemma,
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
select_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
axiomEquality,
hypothesis,
thin,
rename,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesisEquality,
functionEquality,
universeEquality,
dependent_pairFormation,
functionExtensionality,
applyEquality,
independent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
dependent_functionElimination,
equalitySymmetry,
because_Cache,
setElimination,
productElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
independent_pairEquality,
equalityTransitivity,
addEquality
Latex:
\mforall{}[T:Type]. \mforall{}f:T {}\mrightarrow{} T. \mforall{}x,y:T. y is f*(x) supposing x = y
Date html generated:
2018_05_21-PM-07_44_44
Last ObjectModification:
2017_07_26-PM-05_22_17
Theory : general
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