Nuprl Lemma : testsq
λx.(x + 2) ~ λx.(x + 1 + 1)
Proof
Definitions occuring in Statement :
lambda: λx.A[x],
add: n + m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
int_formula_prop_wf,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermAdd_wf,
itermConstant_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
int_subtype_base,
subtype_base_sq
Rules used in proof :
sqequalRule,
sqequalReflexivity,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination
Latex:
\mlambda{}x.(x + 2) \msim{} \mlambda{}x.(x + 1 + 1)
Date html generated:
2016_05_15-PM-07_41_46
Last ObjectModification:
2016_01_16-AM-09_32_44
Theory : general
Home
Index