Nuprl Lemma : grp_op_l
∀[g:GrpSig]. ∀[a,b,c:|g|]. (a * b) = (a * c) ∈ |g| supposing b = c ∈ |g|
Proof
Definitions occuring in Statement :
grp_op: *,
grp_car: |g|,
grp_sig: GrpSig,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
infix_ap: x f y,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
infix_ap: x f y
Lemmas referenced :
equal_wf,
grp_car_wf,
grp_sig_wf,
infix_ap_wf,
grp_op_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
Error :applyLambdaEquality,
applyEquality
Latex:
\mforall{}[g:GrpSig]. \mforall{}[a,b,c:|g|]. (a * b) = (a * c) supposing b = c
Date html generated:
2016_10_21-AM-11_25_17
Last ObjectModification:
2016_07_12-PM-01_05_48
Theory : groups_1
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