Nuprl Lemma : req*_inversion
∀[x,y:ℝ*]. (x = y ⇒ y = x)
Proof
Definitions occuring in Statement :
req*: x = y,
real*: ℝ*,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
req*: x = y,
exists: ∃x:A. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
guard: {T},
real*: ℝ*,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
nat: ℕ,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
req_inversion,
int_upper_subtype_nat,
int_upper_wf,
all_wf,
req_wf,
req*_wf,
real*_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
dependent_pairFormation,
hypothesisEquality,
cut,
hypothesis,
dependent_functionElimination,
introduction,
extract_by_obid,
isectElimination,
applyEquality,
because_Cache,
sqequalRule,
independent_isectElimination,
setElimination,
rename,
lambdaEquality
Latex:
\mforall{}[x,y:\mBbbR{}*]. (x = y {}\mRightarrow{} y = x)
Date html generated:
2018_05_22-PM-03_14_20
Last ObjectModification:
2017_10_06-PM-02_01_32
Theory : reals_2
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