Nuprl Lemma : radd_rcos_functionality
∀[x,y:ℝ]. radd_rcos(x) = radd_rcos(y) supposing x = y
Proof
Definitions occuring in Statement :
radd_rcos: radd_rcos(x),
req: x = y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T,
subtype_rel: A ⊆r B,
uiff: uiff(P;Q),
and: P ∧ Q,
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
radd_rcos_wf,
set_wf,
real_wf,
req_wf,
radd_wf,
rcos_wf,
sq_stable__req,
equal_wf,
req_witness,
req_functionality,
req_weakening,
radd_functionality,
rcos_functionality
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
sqequalRule,
lambdaEquality,
lambdaFormation,
setElimination,
rename,
independent_functionElimination,
imageMemberEquality,
baseClosed,
imageElimination,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
applyEquality,
setEquality,
isect_memberEquality,
because_Cache,
independent_isectElimination,
productElimination
Latex:
\mforall{}[x,y:\mBbbR{}]. radd\_rcos(x) = radd\_rcos(y) supposing x = y
Date html generated:
2016_10_26-PM-00_17_02
Last ObjectModification:
2016_09_12-PM-05_41_16
Theory : reals_2
Home
Index