Nuprl Lemma : rfun-eq_weakening
∀[I:Interval]. ∀[f,g:I ⟶ℝ]. ((f = g ∈ I ⟶ℝ) ⇒ rfun-eq(I;f;g))
Proof
Definitions occuring in Statement :
rfun-eq: rfun-eq(I;f;g),
rfun: I ⟶ℝ,
interval: Interval,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
rfun-eq: rfun-eq(I;f;g),
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
uimplies: b supposing a,
sq_stable: SqStable(P),
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
req_wf,
squash_wf,
true_wf,
real_wf,
r-ap_wf,
i-member_wf,
sq_stable__i-member,
iff_weakening_equal,
req_weakening,
set_wf,
equal_wf,
rfun_wf,
req_witness,
interval_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
independent_isectElimination,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
natural_numberEquality,
universeEquality,
productElimination,
setEquality,
isect_memberEquality
Latex:
\mforall{}[I:Interval]. \mforall{}[f,g:I {}\mrightarrow{}\mBbbR{}]. ((f = g) {}\mRightarrow{} rfun-eq(I;f;g))
Date html generated:
2017_10_03-AM-09_33_40
Last ObjectModification:
2017_07_28-AM-07_51_25
Theory : reals
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