Nuprl Lemma : stable__function_equal
∀[A,B:Type]. ∀[f,g:A ⟶ B]. Stable{f = g ∈ (A ⟶ B)} supposing ∀x:A. Stable{(f x) = (g x) ∈ B}
Proof
Definitions occuring in Statement :
stable: Stable{P},
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
stable: Stable{P},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
and: P ∧ Q,
prop: ℙ,
false: False,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
isect_wf,
all_wf,
not_wf,
equal_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
functionExtensionality,
hypothesis,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
equalitySymmetry,
dependent_set_memberEquality,
independent_pairFormation,
lemma_by_obid,
isectElimination,
functionEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
setEquality,
voidElimination,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[f,g:A {}\mrightarrow{} B]. Stable\{f = g\} supposing \mforall{}x:A. Stable\{(f x) = (g x)\}
Date html generated:
2016_05_13-PM-03_09_31
Last ObjectModification:
2016_01_06-PM-05_27_14
Theory : core_2
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